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Unformatted text preview: π 3 , f changes from negative to positive, so f has a local minimum and f ( 4 π 3 ) =1 √ 3 . 1 (g) Use quotient rule again to ﬁnd f 00 ( x ) = 2 sin x (cos x1) (2 + cos x ) 3 . Because the denomenator > 0, and cos x1 < 0, we know f 00 ( x ) > if sin x < 0, that is, π < x < 2 π . So f is concave up on ( π, 2 π ) and concave down on (0 ,π ). And f has an inﬂection point at ( π, 0) and (0 , 0). (h) Use all the above information, we sketch the graph of the function restricted to [0 , 2 π ]. 1 2 3 4 5 60.60.40.2 0.2 0.4 0.6 We then extended it using periodicity, to complete the graph.105 5 100.60.40.2 0.2 0.4 0.6 2...
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 Fall '06
 McAdam
 Calculus, Derivative, Cos, Mathematical analysis, Convex function

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